Combining Texts
Ideas for
'Precis of 'Limits of Abstraction'', 'Concepts and Counting' and 'Letters to Samuel Masson'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
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A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
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I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
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10530
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Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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